Completeness and limitation of natural languages

Abstract

Expressibility, namely the condition that whatever can be thought can be said, is for strong reasons considered as an essential property of natural languages. To avoid circularity, thought cannot be identified here as what language expresses. The present paper argues that completeness of language with regard to thought is a natural consequence of the fact that the language faculty is essentially the capacity to acquire and use combinatorial systems of symbols. In contrast to iconic signs, symbolic systems do not depend on similarity between signal and meaning, but are based on convention. This symbolic nature of language provides access to any domain of human experience, since no situational connection or similarity between signal and denotatum is required; the combinatorial character allows for any degree of detail, as it provides for expressions of arbitrary complexity. The symbolic and combinatorial nature of human languages implies their discrete and abstract character, by which they are limited to the expression of discrete meanings. Mental structures that are bound to similarity with the signal they rely on are therefore outside the range of language. Percepts of faces and the meaning of music are briefly discussed as mental representations that cannot be verbalized. The symbolic nature of language sets the limits of expressibility, but it also allows for metalanguage and definitions, which in turn are means to overcome local constraints on expressibility. Finally, expressibility is to be distinguished from codability, i.e., the preference for optimal expression and its consequences, which shape conventions and use of symbols.